The design of such vehicle heaters, which are designed, in general, as air or water heaters and are operated for the most part with fuel, may be such that a control device is arranged in the area of a blower, which delivers the combustion air for a burner area and optionally also the heating air that is to be heated. The control device comprises a housing, in which a circuit assembly unit, for example, in the form of a printed circuit board, is accommodated. Such a control device, controlling or regulating the operation of a heater, is connected electrically to a vehicle wiring system via a cable harness, which has a plug at one end area of a cable establishing the wire connection for being plugged into a corresponding receptacle in a vehicle and is connected, in general, rigidly, for example, by soldering, to the circuit assembly unit at its other end area. This cable of the cable harness can be led out of the heater in the area of ducts in the housing of the control device, on the one hand, and in a heater housing, on the other hand, and a plurality of openings may be provided, for example, in the heater housing for passing through the cable.